Explanation

Given:

1. Sum of roots: α + β = 2

2. Sum of cubes of roots: α³ + β³ = 98

Step-by-Step Solution

Step 1: Use the identity for α³ + β³

α³ + β³ = (α + β)³ - 3αβ(α + β)

Step 2: Substitute known values

98 = (2)³ - 3αβ(2)

98 = 8 - 6αβ

Step 3: Solve for αβ

98 - 8 = -6αβ

90 = -6αβ

αβ = -15

Step 4: Form the quadratic equation

x² - (α + β)x + αβ = 0

x² - 2x - 15 = 0

The answer is x² - 2x - 15 = 0.